共查询到20条相似文献,搜索用时 46 毫秒
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With the help of technique of integration within an ordered product (IWOP) of operators we find new integration transformation connecting the coherent state and the biparticle entangled state. We also point out that under this kind of integration transformation the direct product of two single-variable Hermite polynomials behaves quite different from the two-variable Hermite polynomials, in this way we show that the latter is intrinsic to the phase space of quantum entanglement. As a byproduct, some operator identities for theoretical quantum optics can also be neatly expressed in terms of the two-variable Hermite polynomials. 相似文献
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Jun-hua Chen Hong-yi Fan Xu-bing Tang 《International Journal of Theoretical Physics》2012,51(1):14-22
It is known that beamsplitter can be used to produce quantum entanglement, in this paper we examine this topic from the point
of view of Wigner operators. Using Weyl-ordering of the Wigner operator and the Weyl ordering invariance of Weyl ordered operators
under similarity transformation we derive the entanglement rule of Wigner operators at a beamsplitter. 相似文献
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FAN Hong-Yi 《理论物理通讯》2008,50(5):1089-1092
We re-explain the Weyl quantization scheme by virtue of the technique of
integration within Weyl ordered product of operators, i.e., the Weyl
correspondence rule can be reconstructed by classical functions' Fourier transformation followed by an inverse Fourier transformation within Weyl ordering of operators. As an application of this reconstruction, we derive the quantum operator coresponding to the angular spectrum amplitude of a spherical wave. 相似文献
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We find that classical similarity transformations in the coherent state representation projects onto the similarity transformation operators (STO), these operators constitute a loyal representation of symplectic group. Remarkably, the multiplication rule of the STOs naturally leads to the quantum optical generalized ABCD law, which is the quantum mechanical correspondence of the classical optical ABCD law. Throughout the whole derivation, the technique of integration within an ordered product (IWOP) of operators is employed. 相似文献
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FAN Hongyi 《理论物理通讯》1999,31(2):285-290
Dirac expected that his symbolic method (q-number theory) which could express the physical law in neat and concise way would probably get developed. In this paper, we show that the technique of integration within an ordered product of operators can fashion Dirac's symbolic method and develop representation theory and transformation theory of quantum mechanics. 相似文献
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FAN Hong-yi 《理论物理通讯》1989,11(1):93-98
Using the IWOP (integration within ordered product) technique, we construct a new state vector representation in two-mode Fock space. The tensor product of a kind of squeeze operators can then be well identified in the new representation, which manifestly shows that these squeeze operators are quantum maps imaged by certain symplectic transformation in classical phase space. 相似文献
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We study a new type of thermal state which is obtained by operating Hadamard operator on a thermal field. We call this new thermal state as quantum Hadamard’s thermal state (QHTS). The normally ordered form of QHTS is derived by using Weyl-ordering invariance under the similarity transformation and the Weyl correspondence scheme. We find that QHTS can be considered as squeezed state under certain conditions. The statistical properties of QHTS is also discussed. 相似文献
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By virtue of the new technique of performing integration over Dirac’s ket–bra operators, we explore quantum optical version of classical optical transformations such as optical Fresnel transform, Hankel transform, fractional Fourier transform, Wigner transform, wavelet transform and Fresnel–Hadmard combinatorial transform etc. In this way one may gain benefit for developing classical optics theory from the research in quantum optics, or vice-versa. We cannot only find some new quantum mechanical unitary operators which correspond to the known optical transformations, deriving a new theorem for calculating quantum tomogram of density operators, but also can reveal some new classical optical transformations. For examples, we find the generalized Fresnel operator (GFO) to correspond to the generalized Fresnel transform (GFT) in classical optics. We derive GFO’s normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in the context of quantum optics. Especially, the introduction of quantum mechanical entangled state representations opens up a new area in finding new classical optical transformations. The complex wavelet transform and the condition of mother wavelet are studied in the context of quantum optics too. Throughout our discussions, the coherent state, the entangled state representation of the two-mode squeezing operators and the technique of integration within an ordered product (IWOP) of operators are fully used. All these have confirmed Dirac’s assertion: “...for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory”. 相似文献
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The generalized continuous variable two-mode entangled state |ς> is proposed by using the technique of integration within
an ordered product (IWOP) of operators. The characteristics of this new entangled representation and its application in quantum
teleportation are analyzed in detail. These results indicate that such real parameters |ς> indeed make up a new entangled
representation owing to its completeness and orthogonal relation. By employing the |ς> as quantum transmission channel, the
teleportation of any single-mode quantum state 3 |ψ>3 can be realized by a unitary transformation. 相似文献
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李宗诚 《原子与分子物理学报》2008,25(4):977-983
本文探讨建立以环境提供的熵流为自变量的熵变函数;当熵变化取负值时,此函数可称
作有序生成函数。在此基础上,从量子系统为形成并维持有序化的低熵态而由环境提供可转化为物质的能量流或熵流方面考虑量子系统的消耗,建立量子消耗函数;从量子系统经过非平衡相变而由无序化的高熵态转入有序化的低熵态方面考虑量子系统的补偿,建立量子补偿函数;进而在量子消耗和量子补偿之间取剩余,形成量子组织增益量。量子系统总是在一定的消耗下力图达到最大的组织增益,可将这一目标状态看作量子组织均衡(或量子组织平衡)。 相似文献
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Based on the rotation transformation in phase space and
the technique of integration within an ordered product of operators,
the coherent state representation of the multimode phase shifting
operator and one of its new applications in quantum mechanics are
given. It is proved that the coherent state is a natural language
for describing the phase shifting operator or multimode phase
shifting operator. The multimode phase shifting operator is also
a useful tool to solve the dynamic problems of the multimode
coordinate--momentum coupled harmonic oscillators. The exact energy
spectra and eigenstates of such multimode coupled harmonic
oscillators can be easily obtained by using the multimode phase
shifting operator. 相似文献
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In this paper, we introduce a new way to obtain the Q-P (P-Q) ordering of quantum mechanical operators, i.e., from the classical correspondence of Q-P (P-Q) ordered operators by replacing q and p with coordinate and momentum operators, respectively. Some operator identities are derived concisely. As for its applications, the single (two-) mode squeezed operators and Fresnel operator are examined. It is shown that the classical correspondence of Fresnel operator’s Q-P (P-Q) ordering is just the integration kernel of Fresnel transformation. In addition, a new photo-counting formula is constructed by the Q-P ordering of operators. 相似文献